Learning fractions and long division in elementary school leads to math success, according to a Carnegie Mellon research team led by Robert Siegler. In the U.S. and Britain, fifth graders’ understanding of fractions and long division correlated with their ability to learn higher math.

“We need to improve instruction in long division and fractions, which will require helping teachers to gain a deeper understanding of the concepts that underlie these mathematical operations,” said Siegler. “At present, many teachers lack this understanding.” By contrast, East Asian teachers can explain why math operations work.

And college remedial classes are filled with people who never “got” fractions.

In a University of Chicago study students in first and second grade who chose the right shape to complete a square “also showed the most growth in their number-line knowledge over the following school year, and scored highest on a measure of mathematics ability at age eight.”

Parents can help their children develop spatial skills.

. . . Temple University psychology professor Nora Newcombe and her coauthors found that parents and children playing with blocks together were much more likely to use spatial terms like “over,” “around,” and “through,” than participants who played with a pre-assembled toy—and that it’s hearing and voicing such words that helps improve children’s spatial awareness.

Another 2011 study, this one from the University of Chicago, reported that the number of spatial terms (like “circle,” “curvy,” and “edge”) parents used while interacting with their toddlers predicted how many of these kinds of words children themselves produced, and how well they performed on spatial problem-solving tasks at a later age.

My first reaction was that kids who are good at math at a young age are likely to be good at math when they’re older. But there’s got to be more to the research than that, surely.